Electron paramagnetic resonance as a tool to determine the sodium charge storage mechanism of hard carbon

Hard carbon is a promising negative electrode material for rechargeable sodium-ion batteries due to the ready availability of their precursors and high reversible charge storage. The reaction mechanisms that drive the sodiation properties in hard carbons and subsequent electrochemical performance are strictly linked to the characteristic slope and plateau regions observed in the voltage profile of these materials. This work shows that electron paramagnetic resonance (EPR) spectroscopy is a powerful and fast diagnostic tool to predict the extent of the charge stored in the slope and plateau regions during galvanostatic tests in hard carbon materials. EPR lineshape simulation and temperature-dependent measurements help to separate the nature of the spins in mechanochemically modified hard carbon materials synthesised at different temperatures. This proves relationships between structure modification and electrochemical signatures in the galvanostatic curves to obtain information on their sodium storage mechanism. Furthermore, through ex situ EPR studies we study the evolution of these EPR signals at different states of charge to further elucidate the storage mechanisms in these carbons. Finally, we discuss the interrelationship between EPR spectroscopy data of the hard carbon samples studied and their corresponding charging storage mechanism.

We are very grateful to the reviewers for their time and careful consideration of our manuscript.We appreciate their advice in helping us deliver the best possible version of the manuscript.Please find our point-by-point responses to their comments.
1) The most noteworthy highlight of this manuscript rests with the intended distinction of the EPR signal for the 'slope' and 'plateau' capacity ascription of different microstructure in hard carbon.However, the author mainly discussed the characteristic results of pristine materials with different modifications, whereas few results are presented of the discharged hard carbon at different charge/discharge states.This still makes it confuse to reasonably understand the storage mode of sodium ions within hard carbon during exact discharging process.To better support the authors' opinion, in-situ EPR test or more ex-situ EPR results should be furtherly conducted to monitor the evolution of sodium ion storage within hard carbon.
We collected ex situ EPR data for all the samples shown in this study and included a discussion in the manuscript regarding the post-mortem analysis for all these.We also improved the previous ex-situ EPR discussion for the two pristine samples in the manuscript to aid understanding from the readership.has been added to the SI (Table S7), to provide information on g values, peak-topeak linewidth and lineshape fitting information for all the signals obtained during the ex-situ experiments.

Electron
Changes to the manuscript (Page 12, line 12) EPR spectrum of pristine HC700 at 10 K showed an intense and sharp signal with a Lorentzian lineshape centred at g = 2.0024 and ∆Hpp = 9.5 G (Figure 5a) that obeyed the Curie-Weiss law, as expected from localised spin centres (Figure 6a). 38The spin g-factor is close to the g-factor for a free electron (ge = 2.0023), which indicates that the sample has a large spin-orbit coupling constant due to the presence of heteroatoms such as oxygen and nitrogen. 38EPR parameters of the signal are consistent with localised radicals, which can be attributed to a defective carbon structure, such as dangling bonds with terminating oxygen/nitrogen groups (as observed in the XPS data) in the edge of the graphene sheets and/or on the surface of open micropores and vacancies within the graphene sheets. 75,76 ough post-mortem EPR studies at 10 K, we studied the evolution of this resonance during the discharge process at 0.5 and 0.02 V using a constant current of 5 mA g -1 .Postmortem EPR spectra are shown in Figures 7a and c.The EPR signals observed during discharge to 0.5 V and 0.02 V were similar to the initially observed narrow signal fitted to a Lorentzian lineshape in the pristine material, with g values close to 2.003 and Curie-Weiss type behaviour, indicating the nature of localised spins.A progressive line narrowing occurred when decreasing the potential (from 9.48 G for pristine HC700 to 8 G at 0.5 V, and 6.4 G at 0.02 V), in agreement with previous reported works. 33The changes in the linewidth of the HC700 at different potentials may be explained by alterations in the environment of the free radicals related to the differences in the binding energy of defects/functional groups with Na + ions. 68,69 he chemical process reflected in the EPR signals is directly echoed in the electrochemical curves with the presence of a slope, which has been previously explained with the sodiation of the dangling bonds over a range of different energies. 43,44  localised free radicals in pristine HC700 act as electron acceptors towards Na  S7), further revealing an analogous reaction mechanism to HC700.We did not observe an EPR signal related to the presence of metallic or quasi-metallic Na at 0.02 V which might be related to the insertion of Na into the closed pores or Na plating, despite the observance of a small voltage plateau in the first discharge, which has been attributed to these processes (Figure 3c). 17,77 vious ex situ EPR studies have explained the presence of metallic or quasi-metallic Na with the presence of sharp resonances in the spectra.Nevertheless, these signals were observed in HCs synthesised at higher temperatures than 700 °C and thus, with significantly different electrochemical signatures than HC700, including longer plateaus > 100 mAh g -1 . 12,78 Futhermore, data were collected at different electrochemical conditions to those reported in this work, including the over-discharge of the electrode or data collected during the second discharge cycle.Alternatively, it is possible that this signal is weak and overlaps with the narrow signal attributed to the free radicals and therefore it is not possible to overrule this process.

(Page 13, line 20)
Increasing the temperature from 700 °C to 1000 °C led to a drastic reduction of the EPR signal intensity by a factor of 8, which we attributed to the start of the graphitisation process and subsequent recombination of free radicals and removal of defects.A broad signal with an asymmetric (Dysonian) lineshape (A/B= 1.07) (g = 2.0044 and ∆Hpp ≈ 150 G) at 10 K (Figure 5d) and paramagnetic Pauli behaviour was observed (Figure 6c). 74This signal is attributed to the existence of mobile electrons from intrinsic defects from basal planes in the carbon structure, on which electrons can move without limitation. 73,74 43,79,80 hus, an explanation for these observations is that the broad component in the discharged HC1000 sample arises from localised spins when Na + ions are intercalated into the graphitic structure, and the narrow signal is associated to the formation of localized paramagnetic centres after Na adsorbed on the disordered carbon surface. 40This is further supported by the increased broad/narrow ratio and its decreased linewidth feature over the discharging process, as the increased spin concentration at lower voltage causes further linewidth narrowing.Akin to the HC700 ex-situ studies, we could not conclusively determine whether Na quasi-metallic related to Na insertion into the closed pores was present in this sample.
(Page 15, line 3) …..For the ball-milled HC1000 samples, the linewidths of the broader signal exhibited an opposite trend to the HC700 samples, as the linewidth decreased from 150 G (HC1000) to 140 (HC1000-400-2h) and 25 G (HC1000-400-5h) (Figure 5 d-f and Table S6).Ball-milling causes a reduction in the range of the extended aromatic structure, which is accompanied by a change in the spin nature in these samples, i.e., from Pauli to Curie-Weiss law behaviour (Figure 6c).This behaviour might be related to carbon structure degradation, which has proved to be detrimental to the electrochemical performance observed in the HC1000-400-5h sample.Ex-situ EPR studies also reflected this unusual behaviour, where only one signal was observed after discharge to 0.02 V, suggesting one Na storage process related to the slope capacity behaviour.This contrasts with the two signals observed in HC100-400-2h (Figure SI-14) and HC1000 (Figure 7), which featured two different Na storage behaviours which might be attributed to both slope and plateau processes.
For the ball-milled HC1000 samples, the linewidths of the broader signal exhibited an opposite trend to the HC700 samples, as the linewidth decreased from 150 G (HC1000) to 140 (HC1000-400-2h) and 25 G (HC1000-400-5h) (Figure 5 d-f and Table S6).Ball-milling causes a reduction in the range of the extended aromatic structure, which is accompanied by a change in the spin nature in these samples, i.e., from Pauli to Curie-Weiss law behaviour (Figure 6c).This behaviour might be related to carbon structure degradation, which has proved to be detrimental to the electrochemical performance observed in the HC1000-400-5h sample.Ex-situ EPR studies also reflected this unusual behaviour, where  S7. g value, linewidth and lineshape information obtained from the ex-situ EPR spectra measured at 10K.
Sample@ 10K Broad signal Narrow signal 2) The author provided mass raw data in the main text without organized summary and reasonable presentation, which made it hard to be understood and awkward to read.It would be better if the author can furtherly enhance the relationship of different experimental data with more concise logicality and comprehension.
To aid the organisation, comprehension, and presentation of our results we conducted an extensive re-writing of the manuscript.Due to this extensive re-writing, we have not tracked changes in the manuscript related to changes in the writing style and have highlighted in yellow added information or changes that we have added to the manuscript to draw the attention of the reviewer.In particular, we have:

Changes to the manuscript:
-Renamed our samples from B187 and B1810 to HC700 and HC1000, respectively, so the pyrolysis temperature at which these samples were produced can be easily identified by the reader when going through the manuscript.
-Removed two datasets of the manuscript (those related to the B187, and B1810 HCs being milled at 600 rpm for 2h) to focus only on the influence of the ball-milling time (and not the speed) on structure, electrochemistry and EPR data of the HC materials studied.We Electron Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes 7 considered that having these two datasets was making the manuscript longer without adding any value to the general discussion of results, as data were almost identical to that observed for B187 and B1810 at 400 rpm for 2h.
-We have restructured the article by adding several subheadings in the "Results and Discussion" section (see manuscript) and swapped the order of the EPR and electrochemistry section so we could easily explain, and correlate data related to XRD, XPS, Raman, SAXS and BET to the electrochemical behaviour of all the studied materials first, and then we could further relate these with the EPR data, which is the focus of our manuscript.We thought it could have been confusing for the reviewer to find the EPR data first before understanding how the samples perform electrochemically.
-We have updated or incorporated new summary tables and figures in the manuscript that compare and/or combine results from different techniques to aid understanding and have incorporated new discussion to reflect the new data shown in the Figures/Tables.These are: • The average interlayer distance (d002) in both pristine HC700 and HC1000 materials was calculated as 0.38 nm and 0.37 nm, respectively (Table 1).These values are larger than those of graphite (0.33 nm). 48The difference in d002 values between both samples is expected to be small given the carbonisation temperatures used, as previous findings have shown that the d002 values of HCs only begin to significantly decrease above synthesis temperatures of 1400 °C. 28 showing a higher degree of in-plane ordering and a lesser presence of oxygen-containing terminal groups, respectively.This behaviour was analogous to that observed in other HC materials synthesised from biowaste precursors. 17,48 pon extending the milling time, ID1/IG and ID3/IG ratios increased in both cases due to higher defect site concentration and the presence of carbon-oxygen linkages. 26Similarly, La values calculated using Equation S2 indicated a reduction of the graphitic domains upon milling, as expected from particle fragmentation caused by this treatment (Figure 2b).

(Page 7, line 13)-Text discussing B'' trend among all the studied samples
The destruction of some of the closed porosity with the mechanical treatment is responsible for the observed reduction in the surface area of the closed pores (B' in Equation S3) and the relative number of pores (B'' in Equation S5) (Table 1).
• Figure 3c and f and Table S3which summarise slope, plateau and total capacities in the 1 st and 2 nd charge cycles and ICE.Table S3.Slope and plateau capacity values obtained from the 1 st and 2 nd charge processes of the pristine and ball-milled HC700 and HC1000 samples using dQ/dV vs. V curves shown    S5).Furthermore, we included a new  In contrast, our conditions are simpler (as described below) due to the absence of the Li signal.A simulation involving two components is deemed sufficient for our purposes.

Page 5, Methods Section
The EPR lineshape simulation of a single component was performed in MATLAB 1 using the following equation: 9 ) ) ) (Equation S7) where y is the signal intensity, y0 is the background, C is the amplitude factor, x is the magnetic field, xc is the centre magnetic field of the EPR signal, w is the linewidth, a is the ratio of the dispersion to absorption with a range from 0 to 1.If a = 1, the EPR signal is the symmetric Lorentzian lineshape.If a ≠ 1, a Dysonian lineshape is considered.The Dysonian lineshape, with its characteristic asymmetric factor A/B, corresponds to the ratio of intensities of the spectral positive peak to the negative one.
For multi-component spectra fitting, this can be realized by mathematical addition, where ytotal is the sum of individual y components obtained from Equation S7, i.e., ytotal = y1 +y2 We also included a new column, labelled "Lineshape" in Tables S5-S7 to summarise the lineshape fitting used for the different EPR signals observed in the spectra of all the samples.Therefore, this data is not that convincing.It would be better for the author to provide other experimental data like TEM to support their conclusion.
We thank the reviewer for this comment, which allowed us to reflect and improve the discussion regarding the XRD data obtained for our samples in more detail.For reference, the previous text in the initial submission read as follows: Powder X-ray diffraction (PXRD) data of pristine and ball-milled B1810 and B187 samples showed two main broad reflections at 24° and 43.2° 2θ, characteristic for ( 002) and ( 100) Bragg peaks of graphite (Figure SI-3). 17The (002) diffraction peak in pristine B1810 occurs at a higher 2θ angle than in B187, leading to decreased averaged d002 interlayer spacing of the sp 2 carbon layers, as expected from the higher pyrolysis temperature used. 44According to Bragg's law (2dsinθ= nλ), the interlayer distances (d002) in both pristine B1810 and B187 samples were ca.3.72 and 3.81 Å, respectively.These d002 values are much larger than that of graphite (3.33 Å), 45 thus, enabling Na + ion intercalation.No significant changes in the d002 interlayer spacing were found in both samples after the ball-milling treatments used in this work.We observed, however, subtle changes in crystallinity with milling conditions, as shown in earlier reports. 27For example, B1810 showed decreased crystallinity with increasing milling time (B1810-400-5h), as reflected by the increased broadening of the diffraction peaks.1.The new measurement protocol used for the measurement and calculation of the d002 interlayer distance is described in the Methods section of the SI (page 2). Figure SI-4 was included in the SI to show an example of one of the fittings made to calculate d002.Based on the d002 values obtained, now calculated more confidently by us, we concluded that there were minimal differences between all the samples studied in this work.This supports literature findings on d002 values for hard carbon material synthesised at the temperatures described here, which showed very minor differences in d002 values as well as XRD data on ball-milled samples previously reported in the literature.Thus, we added the text below in the manuscript to describe these observations.
Changes to the manuscript (Page 7): Changes to the manuscript (Page 4, line 13): Powder X-ray diffraction (PXRD) data of pristine and ball-milled HC700 and HC1000 samples showed two main broad reflections at ca. 24° and 44° 2θ, which are characteristic of ( 002) and ( 100) Bragg peaks of graphite (Figure SI-3). 12The average interlayer distance (d002) in both pristine HC700 and HC1000 materials was calculated as 0.38 nm and 0.37 nm, respectively (Table 1).These values are larger than those of graphite (0.33 nm). 48The difference in d002 values between both samples is expected to be small given the carbonisation temperatures used, as previous findings have shown that the d002 values of HCs only begin to significantly decrease above synthesis temperatures of 1400 °C. 28 (Page 2, Methods section) "Powder X-ray diffraction (XRD) data were collected on a Rigaku MiniFlex600 at room temperature in Bragg-Brentano geometry with a 0.6 kW Cu-source generator (Kα = 1.54059Å) and a D/teX Ultra detector.All samples were packed on a flat circular plastic insert placed inside a stainless-steel sample holder.To account for differences in sample packing/height, titanium foil was used as a reference for all of the samples.A circular disc of Ti foil was first measured on its own and used as a reference.Subsequent HC powdered samples were packed on top of the Ti foil.Thus, Ti reflections were present in all the X-ray diffraction data.
All the XRD data were shifted so that the most intense Ti reflection was at 38.21 ° 2θ to match that of the pristine Ti foil reference sample.All samples were scanned from 5° to 70° 2θ".All samples were scanned from 5° to 70° 2θ.The average interlayer spacing was calculated according to Bragg's law: where d002 is the average interlayer spacing, θ is the diffraction angle of the ( 002) reflection, λ is the wavelength of the X-ray beam (Cu Kα radiation, 0.154059 nm) and n is the order of the reflection.To find accurately the position of the (002) reflection, a Gaussian peak was fitted to the (002) reflection and an asymmetric least squares smoothing baseline was used using the Origin software. 1An example of such a fitting can be observed in   The definition of the "a1" parameter was provided in the Supplementary information (Page 3).
As reflected in Equation S4 of the SI (Equation S2 in the first submission), D' (diameter of the closed pores) is proportional to a1, and therefore, we find that the D' parameter is more relevant to discuss in the manuscript than the a1 coefficient.Therefore, we prepared a new figure (Figure 2c-shown above) to show trends in this parameter for all the samples.
Nevertheless, we have added in the manuscript a sentence to clarify that a1 and D' are proportional to each other.We also added the definition of a1 in the manuscript.
Changes to the manuscript (Page 7, line 7): The diameter of the closed pores (D') (which is proportional to a1 (size factor related to the radius of a spherical pore, as shown in Equation S4), From the results in the two pictures, negligible divergences lie in the two series samples for their average pore size.
To better highlight the differences in a1 values for the different datasets we have decided to provide these values in Table 1 and remove Figures 1e and j to avoid any confusion by the readership.
Changes to the manuscript (Page 7): Similar conditions also occurred in the Figure 4 d, the authors didn't explain anything for the presented results.
As suggested by Reviewer 1, we have added more discussion in the manuscript related to occurred when decreasing the potential (from 9.48 G for pristine HC700 to 8 G at 0.5 V, and 6.4 G at 0.02 V), in agreement with previous reported works. 33The changes in the linewidth of the HC700 at different potentials may be explained by alterations in the environment of the free radicals related to the differences in the binding energy of defects/functional groups with Na + ions. 68,69 he chemical process reflected in the EPR signals is directly echoed in the electrochemical curves with the presence of a slope, which has been previously explained with the sodiation of the dangling bonds over a range of different energies. 43,44 nges to the manuscript (Page 12, line 7).
In general, localised spins obey Curie-Weiss law, whereby the spin susceptibility (which is proportional to the double integration value of the mass-normalised EPR signal) decreases with increasing temperature; and delocalised electrons will show Pauli behaviour, where the spin susceptibility is independent of the temperature.
6) Results presented in the Figure 6 a and b are reduplicated with the results in Figure 2 and 3.
We assume that Reviewer 1 is referring to Figure 5 from the initial manuscript submission as there was no Figure 6 in the submitted manuscript (?).Figures 5a and b have been now removed from the manuscript.

)
The language should be checked again since there are some typos.
i.e., in the line 150 on page 5, "in HC materials synthesised.71(B187) to 2.01 from other biowaste precursors."; in the line 397 on page 16, "…towards Curie-Weiss behaviour It is therefore not…"; in Figure 5b, the amplification coefficient of the signal tensity for pristine B187 seems not "x50" as the original signal of B187 is much higher than B1810.
Electron Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes

21
The manuscript has been proofread several times by different co-authors and checked against any typos before re-submitting it.The suggested typos were corrected.Before revision (Figure 6)  and c.
After revision Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes 2 New ex-situ EPR spectra for the ball-milled samples can be found in (Figure SI-14) and a new Table Figure SI-14.ex situ EPR measurements of ball-milled (a) HC700 and (b) HC1000 samples when discharged to 0.02 V.

Figure 3 .
Figure 3. Slope and plateau capacity contribution to the total capacity during 1 st charge and 2 nd charge processes for (e) HC700 samples and (f) HC1000 samples.

•
Figures 2a, b and c-which show trends in ID1/IG, La and D' parameters obtained from Raman and SAXS data.

Figure 2 .
Figure 2. (a) ID1/IG and (b) La values calculated from Raman spectroscopy data; and (c) D' values calculated from SAXS data for pristine and ball-milled HC700 and HC1000 samples.

3)
As the fitting of EPR signal is not a general knowledge, the author should interpret the data fitting principle and its detailed fitting process with reasonable equations like what you did for the SAXS data processing or the references published in the journal of Materials Today, 2018, 21, 231-240.Changes to the SI: We have included in the Electron Paramagnetic Resonance (EPR) Spectroscopy section of the SI information re. the fitting of the EPR spectra shown in the manuscript.The fitting shown in the Materials Today paper cited by the Reviewer is much more complex than the fitting used in this paper due to the presence of the Li signal, which causes a phase shift in Electron Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes 13 the overall signal.Consequently, it becomes necessary to isolate the carbon signal within the lithium and carbon mixture.The challenging aspect lies in the fact that the lineshape or asymmetric factor differs in each signal, necessitating calibration and a simulation process, as outlined in the supplementary information in the Materials Today paper.

4)
In the sentence of line 128-129 on page 4, the author claimed that differences exist in the XRD diffraction peaks for the sample of B1810 and B187, however the results presented in the Figure SI-3 showed inexplicit shifts of (002) peak between different samples.Electron Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes 15

FigureFigure SI- 3 .
Figure SI-3.Powder XRD data of pristine and ball-milled (a) HC700 and (b) HC1000 samples.Peaks assigned to the Ti foil have been labelled with a (*) symbol and peaks assigned to zirconium oxide (ZrO2) are labelled with a (△) symbol.The ZrO 2 present in the ball-milled samples is due to the use of ZrO2 balls for the ball-milling procedure.Ti reflections are present as Ti foil was used as reference material to obtain accurate 2θ values for the different samples.

Figure SI- 4 .
Figure SI-4.Example of a fit of the (002) reflection for pristine HC1000 to ascertain the position, FWHM and d002 values.

Figure 4d (
Figure 4d (Figure 7b in the current submission).Figure 7b shows the temperature dependence behaviour of the simulated EPR data for the un-milled HC700 sample when this is discharged to 0.02 V.This Figure is shown to demonstrate that the susceptibility of the sample obeys the Curie-Weiss law (Equation S6) as reflected by the good fit between raw

Figure
Figure5bhas been removed as suggested by the same reviewer in the comment above.

Figure 6 .
Figure 6.Temperature dependence behaviour of the (a, c) broad and (b, d) narrow contributions obtained by lineshape simulation for all the pristine and ball-milled HC700 and HC1000 samples.The double integration (DI) value of the EPR signal is proportional to the spin density and is calculated from the absolute area value of the EPR signal.The solid line in the spectra shows the Curie-Weiss fitting results.(e) Normalised DI value (refers to the spin 447 susceptibility) × T vs. T of the simulated broad signals shown in Figures 6a and c.

Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes
+ , forming covalent C-Na bonds.As the potential decreases, more of these C-Na bonds form, leading to a continuous decrease or even disappearance of original localized radicals in disordered carbons, as previous works have reported.36ThereminiscentEPR signal observed in the spectra after discharge to 0.02 V may be explained by residual bonds which have not reacted with Na.Overall, it was not possible to provide a quantitative measurement of the spins in this study due to difficulties in preserving the electrodes intact during sample Electron 3 preparation.Furthermore, ex situ EPR studies on the two ball-milled HC700 samples after discharge to 0.02 V showed similar EPR signals(Figure SI-14, Table

Table 1 .
Summary Table 1-which summarises relevant parameters from XRD, XPS, Raman, SAXS and BET. of selected structural parameters of pristine and ball-milled HC700 and HC1000 samples obtained from XRD, XPS, Raman, SAXS and BET data.(Page 4, line 15)-Text discussing d002 trend among all the studied samples

Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes
Text discussing ID3/IG trend among all the studied samples Ball-milling these samples resulted only in almost negligible changes in the d002 interlayer spacing (Table 1) and subtle changes in crystallinity with Electron 8 milling conditions (as reflected by the FWHM calculated values for these samples, Table SI-1), as shown in earlier reports. 32(Page 4, line 33)-

Table ( Table S6 )
which summarises g values, linewidth and lineshape information for the EPR signals obtained at 10 K to aid understanding of the EPR data presented in the manuscript.
** D= Dysonian lineshape, the value in brackets indicates the asymmetry parameter A/B, where A and B are the amplitudes of the positive and negative parts of the signal.

Table S5 .
g value, linewidth and lineshape information obtained from the EPR spectra measured at room temperature and shown in Figure S13.* D= Dysonian lineshape, the value in brackets indicates the asymmetry parameter A/B, where A and B are the amplitudes of the positive and negative parts of the signal. *

Table S6 .
g value, linewidth and lineshape information obtained from the EPR spectra measured at 10K shown in Figure 5.
** D= Dysonian lineshape, the value in brackets indicates the asymmetry parameter A/B, where A and B are the amplitudes of the positive and negative parts of the signal.

Table S7
. g value, linewidth and lineshape information obtained from the ex situ EPR spectra measured at 10K.

Table 1 .
Summary of selected structural parameters of pristine and ball-milled HC700 and HC1000 samples obtained fromXRD, XPS, Raman, SAXS and BET data.

32 Electron Paramagnetic Resonance Spectroscopy as a Fast Diagnostic Tool to Determine the Sodium Charge Storage Mechanism of Hard Carbon Anodes 17 Changes to the SI:
Ballmilling these samples resulted only in almost negligible changes in the d002 interlayer spacing (Table 1) and subtle changes in crystallinity with milling conditions (as reflected by the FWHM calculated values for these samples, Table SI-1), as shown in earlier reports.

Table S1 .
Positions of the (002) reflection (in 2θ degrees) and FWHM values of HC700 and HC1000 pristine and ball-milled samples obtained from XRD data shown in

Table 1 .
Summary of selected structural parameters of pristine and ball-milled HC700 and HC1000 samples obtained fromXRD, XPS, Raman, SAXS and BET data.